Russel-Research-Method-in-Anthropology

Bivariate Analysis: Testing Relations 595
Answers to these questions about qualities of a relationship come best from
looking at graphs.
Testing for statistical significance is a mechanical affair—you look up, in
a table, whether a statistic showing covariation between two variables is, or is
not statistically significant. I’ll discuss how to do this for several of the commonly
used statistics that I introduce below. Statistical significance, however,
does not necessarily mean substantive or theoretical importance. Interpreting
the substantive and theoretical importance of statistical significance is anything
but mechanical. It requires thinking. And that’s your job.
The t-Test: Comparing Two Means
We begin our exploration of bivariate analysis with the two-sample t-test.
In chapter 19, we saw how to use the one-sample t-test to evaluate the probability
that the mean of a sample reflects the mean of the population from which
the sample was drawn. The two-sample t-test evaluates whether the means of
two independent groups differ on some variable. Table 20.1 shows some data
that Penn Handwerker collected in 1978 from American and Liberian college
students on how many children those students wanted.
Table 20.2 shows the relevant statistics for the data in table 20.1. (I generated
these with SYSTAT, but you can use any statistics package.)
There are 43 American students and 41 Liberian students. The Americans
wanted, on average, 2.047 children, sd 1.396, SEM 0.213. The Liberians
wanted, on average, 4.951 children, sd 2.387, SEM 0.373.
The null hypothesis, H 0 , is that these two means, 2.047 and 4.951, come
from random samples of the same population—that there is no difference,
except for sampling error, between the two means. Stated another way, these
two means come from random samples of two populations with identical averages.
The research hypothesis, H 1 , is that these two means, 2.047 and 4.951,
come from random samples of truly different populations.
The formula for calculating t for two independent samples is:
t
x 1 x 2
s 2 (1 / n 1 1/n 2 )
Formula 20.1
That is, t is the difference between the means of the samples, divided by the
fraction of the standard deviation, , of the total population, that comes from
each of the two separate populations from which the samples were drawn.
(Remember, we use Roman letters, like s, for sample statistics, and Greek letters,
like , for parameters.) Since the standard deviation is the square root of
the variance, we need to know the variance, 2 , of the parent population.